Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 9 - Section 9.4 - Properties of Logarithms - 9.4 Exercises: 31

Answer

$log_{a}\frac{125}{81}$

Work Step by Step

We know that $log_{b}x^{r}=rlog_{b}x$ (where $x$ and $b$ are positive real numbers, $b\ne1$, and $r$ is a real number). Therefore, $3log_{a}5-4log_{a}3=log_{a}5^{3}-log_{a}3^{4}$. We know that $log_{b}\frac{x}{y}=log_{b}x-log_{b}y$ (where $x$, $y$, and $b$ are positive real numbers and $b\ne1$). Therefore, $log_{a}5^{3}-log_{a}3^{4}=log_{a}\frac{5^{3}}{3^{4}}=log_{a}\frac{125}{81}$.
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